doi: 10.5281/zenodo.17665853
Two-page note: definition of the residue-circulant Laplacian, FFT-based λ₂, Paley gap g(n)=|λ₂−(n−√n)/2|; empirical zeros at primes n≡1 (mod 4) up to 2601. Reproducible; not a primality proof.